Necessary criteria for the Bombieri conjecture
In the paper under review the author considers functionals \(L\) which are the real parts of linear combinations of two Taylor coefficients in the class \(S\) of holomorphic univalent functions \(f(z)=z+\sum_{n=2}^{\infty}a_{n}z^{n}\) in the unit disk. These are related with the Bombieri conjecture in the following way. The Bombieri conjecture can be interpreted in the form that \(L\) are locally maximized by the Koebe function simultaneously in the class \(S\) and on its subclass \(S_{R}\) consisting of typically real functions. The author derives necessary criteria for the Bombieri conjecture in terms of inequalities for solutions to systems of differential equations in variations for the Loewner ODE.
scientific article; zbMATH DE number 7000060
scientific article